Question: Solve for $x$ and $y$ using elimination. ${4x+2y = 52}$ ${5x+2y = 60}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-1$ ${-4x-2y = -52}$ $5x+2y = 60$ Add the top and bottom equations together. ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {4x+2y = 52}\thinspace$ to find $y$ ${4}{(8)}{ + 2y = 52}$ $32+2y = 52$ $32{-32} + 2y = 52{-32}$ $2y = 20$ $\dfrac{2y}{{2}} = \dfrac{20}{{2}}$ ${y = 10}$ You can also plug ${x = 8}$ into $\thinspace {5x+2y = 60}\thinspace$ and get the same answer for $y$ : ${5}{(8)}{ + 2y = 60}$ ${y = 10}$